Implications of positive formulas in modules (RIMS)

TL;DR

This survey explores the significance of implications of positive formulas in module categories, highlighting their algebraic importance and deriving properties based on their specific structures.

Contribution

It provides a comprehensive overview of positive implications in modules, including new and classical examples, and analyzes their properties based on their shape.

Findings

Implications of positive formulas are crucial in understanding module categories.

Properties of these implications depend on their algebraic structure.

The survey includes both classical and recent examples.

Abstract

In this survey the role of implications of positive formulas -- finitary and infinitary -- is dicussed, in general and in module categories, where they seem of particular importance. A list of algebraic examples is given, some old, some rather new, and properties are derived from the particular shape of implications involved.